Given: - Load \( W = 180 \, \text{N} \) - Efficiency \( \eta = 90\% = 0.9 \) - Let the effort \( E \) be applied. The efficiency of a machine is given by the formula: \(\eta = \frac{\text{Mechanical Advantage (MA)}}{\text{Velocity Ratio (VR)}}\) Mechanical Advantage (MA) is defined as the ratio of load to effort: \(\text{MA} = \frac{W}{E}\) Determine the Velocity Ratio (VR) Given that the effort arm is twice the load arm, we can express the Velocity Ratio (VR) as: \(\text{VR} = \frac{\text{Length of effort arm}}{\text{Length of load arm}} = \frac{2L}{L} = 2\) Substitute into the efficiency formula Substituting the expressions for MA and VR into the efficiency formula gives: \(0.9 = \frac{\frac{W}{E}}{2}\) Rearrange to find the effort \( E \) Multiplying both sides by \( 2E \): \(1.8E = W\) Substituting \( W = 180 \, \text{N} \): \( 1.8E = 180\) Solve for \( E \) Now, dividing by 1.8: \(E = \frac{180}{1.8} = 100 \, \text{N}\) Therefore, the effort applied by the machine is: \(\boxed{100 \, \text{N}}\).